UPSC Prelims 2014·CSAT·Quantitative Aptitude·Time, Speed and Distance

A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr then he reaches the factory 7 minutes early the distance of the factory from his house is

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Last updated 23 May 2026, 3:31 pm IST
  1. A3 km
  2. B4 km
  3. C5 kmCorrect
  4. D6 km

Explanation

Let D be the distance from the house to the factory and T be the scheduled time to reach the factory (in hours). 1. When the speed is 5 km/hr, the worker is 3 minutes late. Time taken = D/5 hours. So, D/5 = T + 3/60 (Equation 1) 2. When the speed is 6 km/hr, the worker is 7 minutes early. Time taken = D/6 hours. So, D/6 = T - 7/60 (Equation 2) Subtract Equation 2 from Equation 1: (D/5) - (D/6) = (T + 3/60) - (T - 7/60) (6D - 5D) / 30 = T + 3/60 - T + 7/60 D/30 = 10/60 D/30 = 1/6 Now, solve for D: D = (1/6) * 30 D = 5 km Thus, the distance of the factory from his house is 5 km. The final answer is C
Quantitative Aptitude: A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a spee
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